Mlr

Purpose

Multiple Linear Regression for multivariate Y.

Synopsis

model = mlr(x,y,options)

pred = mlr(x,model,options)

valid = mlr(x,y,model,options)

mlr  % Launches analysis window with MLR as the selected method.

Description

MLR identifies models of the form Xb = y + e.

Inputs

• y = X-block: predictor block (2-way array or DataSet Object)

• y = Y-block: predictor block (2-way array or DataSet Object)

Outputs

• model = scalar, estimate of filtered data.

• pred = structure array with predictions

• valid = structure array with predictions

Options

options = a structure array with the following fields.

• display: [ {'off'} | 'on'] Governs screen display to command line.

• plots: [ 'none' | {'final'} ] governs level of plotting.

• ridge: [ 0 ] ridge parameter to use in regularizing the inverse.

• preprocessing: { [] [] } preprocessing structure (see PREPROCESS).

• blockdetails: [ 'compact' | {'standard'} | 'all' ] level of detail (predictions, raw residuals, and calibration data) included in the model.

• ‘Standard’ = the predictions and raw residuals for the X-block as well as the X-block itself are not stored in the model to reduce its size in memory. Specifically, these fields in the model object are left empty: 'model.pred{1}', 'model.detail.res{1}', 'model.detail.data{1}'.
• ‘Compact’ = for this function, 'compact' is identical to 'standard'.
• 'All' = keep predictions, raw residuals for both X- & Y-blocks as well as the X- & Y-blocks themselves.

Studentized Residuals

From version 8.8 onwards, the Studentized Residuals shown for MLR Scores Plot are now calculated for calibration samples as:

 MSE   = sum((res).^2)./(m-1);
 syres = res./sqrt(MSE.*(1-L));

where res = y residual, m = number of samples, and L = sample leverage. This represents a constant multiplier change from how Studentized Residuals were previously calculated. For test datasets, where pres = predicted y residual, the semi-Studentized residuals are calculated as:

 MSE   = sum((res).^2)./(m-1);
 syres = pres./sqrt(MSE);

This represents a constant multiplier change from how the semi-Studentized Residuals were previously calculated.

See Also

analysis, crossval, ils_esterror, modelstruct, pcr, pls, preprocess, ridge, testrobustness